Delta-sigma modulator

ABSTRACT

Provided is a delta-sigma modulator including a summer summing an input signal and an analog signal, a first integrator integrating an output signal from the summer and outputting a first integration signal, a second integrator integrating the first integration signal and outputting a second integration signal, a comparator comparing the second integration signal and a reference signal and outputting a digital signal according to the comparison result, and a digital-to-analog converter converting the digital signal into an analog signal in response to a clock signal and outputting the converted analog signal, wherein the second integrator operates based on an Nth order (where N is natural number of 1 or greater) transfer function.

CROSS-REFERENCE TO RELATED APPLICATIONS

This U.S. non-provisional patent application claims priority under 35U.S.C. §119 of Korean Patent Application No. 10-2014-0004103, filed onJan. 13, 2014, the entire contents of which are hereby incorporated byreference.

BACKGROUND OF THE INVENTION

The present invention disclosed herein relates to a delta-sigmamodulator, and more particularly, to a delta-sigma modulator having acontinuous-time structure.

A delta-sigma modulator may be implemented in a discrete-time scheme ora continuous-time scheme. A delta-sigma modulator according to thediscrete-time scheme stores and delivers an input signal in a chargetype on the basis of a switched-capacitor scheme. While thediscrete-time delta-sigma modulator operates according to a samplingprocess for an input signal, the continuous-time delta-sigma modulatormay operate without a sampling process for an input signal.

Compared to the discrete-time scheme, the continuous-time scheme has alow requirement for a design of an amplifier used for an integrator andmay operate in low power and high speed. When the integrator does notperform a sampling operation, the continuous-time delta-sigma modulatorhas an anti-aliasing filter effect.

According to characteristics of a high signal to noise ratio (SNR), thecontinuous-time delta-sigma modulator may be used for a wirelesscommunication system, such as a 3rd generation partnership project(3GPP), long term evolution (LTE), and worldwide interoperability formicrowave access (WiMAX).

In addition, delta-sigma modulators having an identical samplingfrequency may use a scheme for increasing an order and output level forenhancing the SNR characteristics. For example, when an order of thedelta-sigma modulator is increased to a 1st, 2nd, and 3rd-order, slopesof a noise transfer function (NTF) of the delta-sigma modulator arerespectively increased to 20 dB/dec, 40 dB/dec. 60 dB/dec. Accordingly,a noise amount within a signal band may be reduced and SNRcharacteristics may be increased.

However, when an order of the delta-sigma modulator for increasing anSNR is increased, the number of integrators is also necessary to beincreased according to the increase of the order. However, powerconsumption is also increased along with the increase of the number ofintegrators, and the number of digital-to-analog converters (DACs)connected back to the integrators is also increased. Accordingly, acircuit of the delta-sigma modulator becomes complex.

SUMMARY OF THE INVENTION

The present invention provides a delta-modulator of which powerconsumption can be lowered despite of an increase of an order.

Embodiments of the present invention provide delta-sigma modulatorsincluding: a summer summing an input signal and an analog signal; afirst integrator integrating an output signal from the summer andoutputting a first integration signal; a second integrator integratingthe first integration signal and outputting a second integration signal;a comparator comparing the second integration signal and a referencesignal and outputting a digital signal according to the comparisonresult; and a digital-to-analog converter converting the digital signalinto an analog signal in response to a clock signal and outputting theconverted analog signal, wherein the second integrator operates based onan Nth order (where N is natural number of 1 or greater) transferfunction.

In other embodiments of the present invention, delta-sigma modulatorsinclude: a summer summing an input signal and an analog signal; a firstintegrator integrating an output signal of the summer and outputting afirst integration signal; a second integrator integrating the firstintegration signal and outputting a second integration signal; azero-optimizer adjusting a transfer function of the second integrator onthe basis of positions of a plurality of zeros; a comparator comparingthe second integration signal and a reference signal and outputting adigital signal according to the comparison result; and a digital-toanalog converter converting the digital signal into an analog signal inresponse to a clock signal and outputting the analog signal; wherein thesecond integrator operates based on an Nth order (where N is a naturalnumber of 1 or greater) transfer function and the zero-optimizercomprises the plurality of zeros corresponding to an order of the secondintegrator.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the present invention, and are incorporated in andconstitute a part of this specification. The drawings illustrateexemplary embodiments of the present invention and, together with thedescription, serve to explain principles of the present invention. Inthe drawings:

FIG. 1 is a block diagram illustrating a typical delta-sigma modulator;

FIG. 2 is a circuit diagram illustrating a delta-sigma modulatoraccording to an embodiment of the present invention;

FIG. 3 is a circuit diagram illustrating a second integrator of FIG. 2;

FIG. 4 is a graph showing SNR output characteristics of the delta-sigmamodulator shown in FIG. 2;

FIG. 5 is a block diagram illustrating a delta-sigma modulator accordingto another embodiment of the present invention;

FIG. 6 is a block diagram illustrating a second integrator connected tothe zero-optimizer in FIG. 5; and

FIG. 7 is a graph showing SNR characteristics of the delta-sigmamodulator in FIG. 5.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Preferred embodiments of the present invention will be described belowin more detail with reference to the accompanying drawings. The presentinvention may, however, be embodied in different forms and should not beconstructed as limited to the embodiments set forth herein. Rather,these embodiments are provided so that this disclosure will be thoroughand complete, and will fully convey the scope of the present inventionto those skilled in the art. In the description of the drawings, likereference numerals are used to denote like constituent elements. Adelta-sigma modulator to be described below and an operation performedthereby are just preferable examples for the purpose of illustrationsonly, not intended to limit the scope of the present invention, so itshould be understood that other equivalents and modifications could bemade thereto without departing from the spirit and scope of the presentinvention.

Hereinafter, it will be described about an exemplary embodiment of thepresent invention in conjunction with the accompanying drawings.

In the description of the present invention, a delta-sigma modulator maybe implemented in a continuous-time scheme and have a negative feedbackstructure that an output of a comparator is connected to a first summer.In addition, in the description of the present invention, a delta-sigmamodulator may be explained as a 3rd-order delta-sigma modulator, but isnot limited thereto and may be implemented in a various order.

FIG. 1 is a block diagram illustrating a typical delta-sigma modulator.Referring to FIG. 1, a delta-sigma modulator 100 includes first to thirdsummers 110, 150, and 170, first to third integrators 120, 140, and 160,a gain converting unit 130, a comparator 180, and a DAC 190. Thesigma-delta modulator 100 shown in FIG. 1 operates based on a feedforward scheme and has the smaller number of DACs compared to the numberof integrators.

The first summer 110 receives an analog input signal Vin inputexternally and an output signal of the DAC 190. The first summer 110delivers, to the first integrator 120, a first sum signal that theoutput signal of the DAC 190 is subtracted from the received inputsignal Vin.

The first integrator 120 receives the first sum signal from the firstsummer 110, and generates a first integration signal by integrating thereceived first sum signal. The first integrator 120 may reduce aquantization error of a digital signal output from the comparator 180through an integration operation. The first integrator 120 delivers thefirst integration signal to first and second gains units 131 and 132,and the second integrator 140.

The gain converting unit 130 may multiply the first integration signaloutput from the first integrator 120 by first and second forwardcoefficients and output the multiplied result. In detail, the gainconverting unit 130 includes first and second gain units 131 and 132.The first gain unit 131 may deliver a first gain signal that the firstintegration signal is multiplied by a preset first forward coefficientto the second summer 150. The second gain unit 132 may deliver a secondgain signal that the first integrating signal is multiplied by a presetsecond forward coefficient to the third summer 170.

The second integrator 140 integrates the first integration signal togenerate a second integration signal, and delivers the generated secondintegration signal to the second summer 150. That is, the secondintegrator 140 further integrates the first integration signal andfurther reduces the quantization error of the digital signal output fromthe comparator 180.

The second summer 150 generates a second sum signal by summing thesecond integration signal and the first gain signal. The second summer150 delivers the generated second sum signal to the third integrator160.

The third integrator 160 generates a third integration signal byintegrating the second sum signal and delivers the generated thirdintegration signal to the third summer 170. Similarly, the thirdintegrator 160 may further reduce the quantization error of the digitalsignal output from the comparator 180 by further integrating the secondintegration signal.

The third summer 170 generates a third sum signal by summing the thirdintegration signal and the second gain signal, and delivers thegenerated third sum signal to the comparator 180.

The comparator 180 compares the received third integration signal with areference signal according to resolution to output an N bit digitalsignal Vout. For example, the comparator 180 may output a 1 bit digitalsignal Vout. The 1 bit comparator may determine a high or low signal bycomparing the third sum signal with 0. The comparator 180 delivers theoutput digital signal Vout to the DAC 190.

The DAC 190 receives the digital signal Vout and converts the receiveddigital signal Vout into an analog signal in response to an externalclock signal. The DAC 190 delivers the converted analog signal to thefirst summer 110. The delta-sigma modulator 100 may be a negativefeedback structure that subtracts a signal output from the DAC 190 fromthe input signal Vin through the first summer 110.

As described above, the 3rd-order delta-sigma modulator 100 shown inFIG. 1 may operate as a DAC through coefficient conversion based onforward coefficients of the gain converting unit 130. However, thedelta-sigma modulator 100 requires the number of integrators tocorrespond to the order and accordingly the circuit becomes complex. Forexample, when the delta-signal modulator 100 is implemented in a3rd-order, three integrators are necessary.

FIG. 2 is a circuit diagram illustrating a delta-sigma modulatoraccording to an embodiment of the present invention. Referring to FIGS.1 and 2, the delta-sigma modulator 200 includes a summer 210, a firstintegrator 220, a second integrator 230, a comparator 240, and a DAC250. In the description of the present invention, the delta-sigmamodulator 200 may be implemented in a 3rd-order delta-sigma modulator,but is not limited thereto and may be implemented in various orders.

Compared to the delta-sigma modulator 100 shown in FIG. 1, thedelta-sigma modulator 200 according to the present invention may includethe second integrator 230 having a single input, single output (SISO)structure. The second integrator 230 may replace the gain converter 130,the second and third summers 150 and 170, and the second and thirdintegrators 140 and 160 based on an Nth order transfer function. Thatis, the second integrator 230 may have an Nth transfer function throughthe coefficient conversion of elements of FIG. 1.

For example, for the transfer function of the second integrator 230, thesecond integrator 230 may be implemented with a 2nd-order transferfunction based on transfer functions of the second and third integrators140 and 160 shown in FIG. 1. It is assumed that, as shown in FIG. 1, thefirst forward coefficient of the first gain unit 131 included in thegain converting unit 130 is C1, and the second forward coefficient ofthe second gain unit 132 is C2. In addition, it is also assumed that atransfer function according to the second integrator 140 is A/s, and atransfer function according to the third integrator 160 is B/s.

$\begin{matrix}\frac{{K\; 1S^{2}} + {K\; 2S} + {K\; 3}}{S^{2}} & (1)\end{matrix}$

The second integrator 230 according to the present invention may have a2^(nd)-order transfer function based on the Equation (1) through thecoefficient conversion. Here, a coefficient K1 may be C2, which is asecond forward coefficient. A coefficient K2 may be multiplication of B,which is a transfer function coefficient of the third integrator 160,and C1 which is a first forward coefficient. In addition, a coefficientK3 is multiplication of A, which is a transfer function coefficient ofthe second integrator 140, and B which is a transfer function of thethird integrator 160.

Through the above-described conversion process, the delta-sigmamodulator 200 according to the present invention may operate with twointegrators, which is different from an existing 3rd-order delta-sigmamodulator scheme requiring three integrators. Furthermore, as the numberof the integrators becomes smaller, power consumption of an entirecircuit may be reduced and a circuit becomes simple.

In the description of the present invention, a 3rd-order delta-sigmamodulator is exemplified but the present invention is not limitedthereto. That is, a 4th-order delta-sigma modulator may operate with twointegrators. Here, the transfer function of the second integrator may beimplemented in a 3rd-order transfer function according to threeintegrators.

For an operation of the delta-sigma modulator 200, the summer 210delivers a sum signal that an output signal of the DAC 250 is subtractedfrom the input signal Vin to the first integrator 220.

The first integrator 220 receives a first sum signal from the firstsummer 210 and generates a first integration signal by integrating thereceived first sum signal. The first integrator 220 may reduces thequantization error of the digital signal output from the comparator 180.

The second integrator 230 integrates the first integration signal togenerate a second integration signal, and delivers the generated secondintegration signal to the comparator 250. That is, the second integrator230 further integrates the first integration signal and reduces thequantization error of the digital signal output from the comparator 250.

The comparator 240 compares the received second integration signal and areference signal according to resolution, and outputs an N bit digitalsignal Vout.

The DAC 250 receives the digital signal Vout and converts the receiveddigital signal Vout into an analog signal in response to an externalclock signal. The analog signal is delivered to the summer 210.Similarly to the delta-sigma modulator 100 shown in FIG. 1, thedelta-sigma modulator 200 may have a negative feedback structure thatsubtracts an output signal of the DAC 250 from the input signal Vin.

As described above, the delta-sigma modulator 200 includes a singleintegrator having a SISO structure, and accordingly a circuit structurethereof may become simpler and power consumption thereof becomesreduced.

FIG. 3 is a circuit diagram illustrating the second integrator shown inFIG. 2. As described in relation to FIG. 2, in order to implement anintegrator having a SISO structure, a 2rd-order integrator is necessaryto be implemented according to a 2rd-order transfer function.

Referring to FIG. 3, the second integrator 230 may output a secondintegration signal Vo based on the 2rd-order transfer function inresponse to positive and negative signals Vi and −Vi of the firstintegration signal output from the first integrator 220 (See FIG. 2).For example, each of the first and second integration signals may beoutput as positive and negative signals according to a differentialamplification structure.

In detail, the second integrator 230 includes first to third resistorsR1, R2, and R3, first and second capacitors C1 and C2, and an amplifier231.

The first resistor R1 is positioned between a positive signal terminalof the first integration signal and a first node T1. The second resistorR2 and the first capacitor C1 are serially connected and positionedbetween the first and second nodes T1 and T2. In addition, the secondcapacitor C2 is positioned between an output terminal of the amplifier231 and the second node T2.

The amplifier 231 may compare amplitudes of a voltage signal of thefirst node T1 and a ground voltage received from the ground terminal,and output the second integration signal Vo by amplifying the comparisonresult. That is, the amplifier 231 may transfer an input signal Vi to anoutput Vo with respect to the transfer function of Equation (2). In anembodiment, the amplifier 231 may be implemented with a differentialamplifier.

$\begin{matrix}{\frac{V_{o}}{V_{1}} = {- \frac{{s^{2} \cdot \left( \frac{R_{1}}{R_{3}} \right)} + {s \cdot \left( \frac{{C_{1}R_{1}} + {C_{2}R_{2}} + {C_{1}R_{2}} - {C_{1}R_{3}}}{C_{1}C_{2}R_{2}R_{3}} \right)} + \frac{1}{C_{1}C_{2}R_{2}R_{3}}}{S^{2}}}} & (2)\end{matrix}$

2nd-order transfer function characteristics of the second integrator 230may be determined based on Equation (2). As described-above, thedelta-sigma modulator 200 may reduce the number of integrators accordingto the 3rd-order delta-sigma modulator due to the second integrator 230operated based on the 2nd-order transfer function. In addition, thesecond integrator 230 is described based on the 2nd-order transferfunction, but is not limited thereto. The transfer function may bechanged according to the order of the second integrator 230.

FIG. 4 is a graph showing SNR output characteristics of the delta-sigmamodulator shown in FIG. 2. A horizontal axis denotes a frequency and avertical axis denotes a decibel (dB). Referring to FIG. 4, a SNRaccording to output characteristics of the delta-sigma modulator 200(see FIG. 2) is about 62 dB, and it can be known that an SNR is obtainedwithin a predetermined range, compared to the delta-sigma modulator 100(see FIG. 1) shown in FIG. 1.

As described above, the delta-sigma modulator 200 may obtain SNRcharacteristics according to low power operation by including anintegrator according to an Nth transfer function.

FIG. 5 is a block diagram illustrating a delta-sigma modulator accordingto another embodiment of the present invention. Referring to FIG. 5, adelta-sigma modulator 300 includes a first summer 310, first and secondintegrators 320 and 340, a second summer 330, a zero-optimizer 350, acomparator 360, and a DAC 370.

That is, the delta-sigma modulator 300 further includes thezero-optimizer 350, compared to the delta-sigma modulator 200 shown inFIG. 2. Operation characteristics of the delta-sigma modulator 200 andthe delta-sigma modulator 300 except the zero-optimizer 200 may beidentical.

In an embodiment, as the second integrator 340 is implemented with the2nd-order transfer function, the delta-sigma modulator 300 may increaseSNR characteristics by adding the zero-optimizer 350. The zero-optimizer350 may adjust arrangement of zeros and poles to fixed values andvariable values, respectively, in response to the second integrationsignal output from the second integrator 330.

For example, the zero-optimizer 350 may include two zeros on the basisof the 2nd-order transfer function. The zero-optimizer 350 may reducenoise according to output characteristics by positioning one zero at anoriginal point and setting a position of the other zero. As the order ofthe transfer function according to an order of the integrator isincreased, the number of zeros may be increased. Typically, as thenumber of zeros is increased, noise according to SNR outputcharacteristics can be further reduced.

FIG. 6 is a circuit diagram illustrating a second integrator to whichthe zero-optimizer of FIG. 5 is connected. Referring to FIGS. 5 and 6,the second integrator 330 may output the second integration signal Vobased on the 2nd-order transfer function in response to positive andnegative signals Vi and −Vi of the first integration signal output fromthe first integrator 320. Similarly, the second integration signal Vomay be output as positive and negative signals Vo and −Vo.

In detail, compared to the second integrator 230 shown in FIG. 3, thesecond integrator 330 further includes fourth and fifth resistors and aninverter 332 having a connection structure of the zero-optimizer 350.

The first resistor R1 positioned between a terminal of a positive signalVi of the first integration signal and a first node T1. The secondresistance R2 and the first capacitor C1 are serially connected andpositioned between the second and third nodes T2 and T3. The thirdresistor R3 is positioned between a terminal of a negative signal −Vi ofthe first integration signal and the third node T3. The second capacitorC2 is positioned between the third node T3 and a fourth node T4.

The amplifier 331 may receive a voltage signal of the first node T1 andamplify a difference between magnitudes of the received voltage signalof the first node T1 and the ground voltage. That is, the amplifier 331may transfer an input signal Vi to an output Vo with respect to thetransfer function of Equation (3). In an embodiment, the amplifier 331may be implemented with a differential amplifier.

The zero-optimizer 350 for improving SNR characteristics may includefourth and fifth resistors. The zero-optimizer 350 may be electricallyconnected to the second integrator 330. In detail, the fourth resistorR4 is positioned between the second node T2 and a fourth node, and thefourth node may be electrically connected to an output terminal of theamplifier 331. The fifth resistor R5 is serially connected to theinverter 332, and positioned between the third node T3 and an outputterminal of the amplifier 331. For example, the inverter 332 may operatein response to a negative signal −Vo of the second integration signaloutput from the amplifier 331.

$\begin{matrix}{\frac{Vo}{Vi} = {- \frac{{K\; 1*S^{2}} + {K\; 2*S} + {K\; 3}}{S^{2} + {K\; 4*S} + {K\; 5}}}} & (3)\end{matrix}$

Referring to Equation (3), a transfer function (Vo/Vi) of the secondintegrator 330 may be obtained. In addition, first to fifth coefficients(K1, K2, K3, K4, and K5) shown in Equation (3) may be obtained throughEquations 4 to 7.

$\begin{matrix}{{K\; 1} = \frac{C\; 1C\; 2R\; 1R\; 2R\; 4R\; 5}{{C\; 1C\; 2R\; 1R\; 2R\; 3R\; 5} + {C\; 1C\; 2R\; 2R\; 3R\; 4R\; 5}}} & (4)\end{matrix}$

First, a first coefficient K1 shown in equation (3) may be obtainedthrough Equation 4.

$\begin{matrix}{{K\; 2} = \frac{\begin{matrix}\left( {{C\; 1R\; 2R\; 3R\; 4} + {C\; 1R\; 1R\; 4R\; 5} +} \right. \\\left. {{C\; 2R\; 2R\; 4R\; 5} + {C\; 1R\; 1R\; 2R\; 4} - {C\; 1R\; 3R\; 4R\; 5}} \right)\end{matrix}}{{C\; 1C\; 2R\; 1R\; 2R\; 3R\; 5} + {C\; 1C\; 2R\; 2R\; 3R\; 4R\; 5}}} & (5)\end{matrix}$

Furthermore, a second coefficient K2 shown in equation (3) may beobtained through Equation (5).

$\begin{matrix}{{K\; 3} = \frac{\left( {{R\; 4R\; 5} + {R\; 2R\; 4}} \right)}{{C\; 1C\; 2R\; 1R\; 2R\; 3R\; 5} + {C\; 1C\; 2R\; 2R\; 3R\; 4R\; 5}}} & (6)\end{matrix}$

In addition, a third coefficient K3 shown in equation (3) may beobtained through Equation (6).

$\begin{matrix}{{K\; 4} = \frac{\begin{matrix}\left( {{C\; 1R\; 2R\; 3R\; 5} + {C\; 1R\; 1R\; 3R\; 5} +} \right. \\\left. {{C\; 2R\; 2R\; 3R\; 5} + {C\; 1R\; 1R\; 2R\; 3} - {C\; 1R\; 2R\; 3R\; 4}} \right)\end{matrix}}{{C\; 1C\; 2R\; 1R\; 2R\; 3R\; 5} + {C\; 1C\; 2R\; 2R\; 3R\; 4R\; 5}}} & (7)\end{matrix}$

In addition, a fourth coefficient K4 shown in equation (3) may beobtained through Equation (7).

$\begin{matrix}{{K\; 5} = \frac{\left( {{R\; 3R\; 5} + {R\; 2R\; 3}} \right)}{{C\; 1C\; 2R\; 1R\; 2R\; 3R\; 5} + {C\; 1C\; 2R\; 2R\; 3R\; 4R\; 5}}} & (8)\end{matrix}$

Finally, a fifth coefficient K5 shown in equation (3) may be obtainedthrough Equation (8).

As described above, the transfer function characteristics according toan operation of the second integrator 330 may be obtained based onEquation (2). In particular, noise according to an output of the secondintegrator 330 may be improved by a structure of the zero-optimizer 350,namely, the fourth and fifth resistors, which are electrically connectedto the second integrator 330.

FIG. 7 is a graph showing SNR output characteristics of a delta-sigmamodulator shown in FIG. 5. A horizontal axis denotes a frequency and avertical axis denotes a decibel (dB).

Referring to FIGS. 5 and 7, the delta-sigma modulator 300 is implementedwith a 3rd-order delta-sigma modulator, and includes a zero-optimizer350 (see FIG. 5) connected to the second integrator 330. The delta-sigmamodulator 300 may increase SNR characteristics compared to thedelta-sigma modulator 200 shown in FIG. 2 according to operationcharacteristics of the zero-optimizer 350.

For example, the delta-sigma modulator 300 may include three zeros andthree poles by including the zero-optimizer 350. In particular, twozeros are positioned at an original point, and the remnant one zero maybe positioned at a pointer A. In response to the zero-optimizer 350, onezero is positioned at the pointer A and accordingly SNR noisecharacteristics may be reduced. Here, the zero position according to thezero-optimizer 350 is described as the pointer A, but is not limitedthereto.

As described above, the delta-sigma modulator 300 can change the noisetransfer function of the system through a position change of the zeropoint according to the zero-optimizer 350.

According to the embodiments of the present invention, a delta-sigmamodulator can operate as a predetermined integrator and a digital-toanalog converter in correspondence to an increase of an order thereof.Accordingly, power consumption can be reduced according to an operationof the delta-sigma modulator.

The above-disclosed subject matter is to be considered illustrative, andnot restrictive, and the appended claims are intended to cover all suchmodifications, enhancements, and other embodiments, which fall withinthe true spirit and scope of the present invention. Thus, to the maximumextent allowed by law, the scope of the present invention is to bedetermined by the broadest permissible interpretation of the followingclaims and their equivalents, and shall not be restricted or limited bythe foregoing detailed description.

What is claimed is:
 1. A delta-sigma modulator comprising: a summersumming an input signal and an analog signal; a first integratorintegrating an output signal from the summer and outputting a firstintegration signal; a second integrator integrating the firstintegration signal and outputting a second integration signal; acomparator comparing the second integration signal and a referencesignal and outputting a digital signal according to the comparisonresult; and a digital-to-analog converter converting the digital signalinto an analog signal in response to a clock signal and outputting theconverted analog signal, wherein the second integrator operates based onan Nth order (where N is natural number of 1 or greater) transferfunction, and wherein, when the second integrator operates based on a2nd-order transfer function, the second integrator comprises: a firstresistor positioned between a positive signal terminal of the firstintegration signal and a first node; a second resistor and a firstcapacitor serially connected between the first node and a second node; athird resistor positioned between a negative signal terminal of thefirst integration signal and the second node; an amplifier comparingmagnitudes between a voltage signal from the first node and a groundsignal and outputting the compared result; and a second capacitor ispositioned between the second node and the amplifier.
 2. The delta-sigmamodulator of claim 1, wherein the digital signal output from thecomparator is delivered to the summer through the digital-to-analogconverter as a negative feedback structure.
 3. The delta-sigma modulatorof claim 1, wherein each of the first and second integration signalscomprises positive and negative signals.
 4. The delta-sigma modulator ofclaim 1, wherein the amplifier is a differential operational amplifier.5. The delta-sigma modulator of claim 1, wherein the summer, the firstand second integrators, the comparator, and the digital-analog converterare implemented in a continuous-time system.
 6. A delta-sigma modulatorcomprising: a summer summing an input signal and an analog signal; afirst integrator integrating an output signal of the summer andoutputting a first integration signal; a second integrator integratingthe first integration signal and outputting a second integration signal;a zero-optimizer adjusting a transfer function of the second integratoron the basis of positions of a plurality of zeros; a comparatorcomparing the second integration signal and a reference signal andoutputting a digital signal according to the comparison result; and adigital-to analog converter converting the digital signal into an analogsignal in response to a clock signal and outputting the analog signal;wherein the second integrator operates based on an Nth order (where N isa natural number of 1 or greater) transfer function and thezero-optimizer comprises the plurality of zeros corresponding to anorder of the second integrator.
 7. The delta-sigma modulator of claim 6,wherein each of the first and second integration signals comprisesnegative and positive signals.
 8. The delta-sigma modulator of claim 7,wherein, when the second integrator operates based on a 2nd-ordertransfer function, the second integrator comprises: a first resistorpositioned between a positive signal terminal of the first integrationsignal and a first node; a second resistor and a first capacitorserially connected between a second node and a third node, wherein thefirst node and second node are serially connected; a third resistorpositioned between a negative signal terminal of the first integrationsignal and the third node; an amplifier comparing magnitudes between avoltage signal of the first node and a ground signal and outputting thecompared result; and a second capacitor positioned between the thirdnode and a fourth node, wherein the fourth node and an output terminalof the amplifier are electrically connected, a fourth resistor ispositioned between the second and fourth nodes, and a fifth resistorpositioned between the third node and the amplifier on the basis of theplurality of zeros.
 9. The delta-sigma modulator of claim 8, furthercomprising an inverter serially connected to the fifth resistor on thebasis of the negative signal of the second integration signal.